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The probability of "I found one on the beach today"¶

Roger Erismann, Romain Tramoy, Bhavish Patel, Montserrat Filella

Affiliations

Roger Erismann - Hammerdirt, Brugstrasse 39, CH-2503 Biel, Switzerland

Romain Tramoy - Laboratoire Eau Environment et Systèmes Urbains (LEESU), 61 Av. du Général de Gaulle, F-94000 Créteil, France

Bhavish Patel - Paul Scherer Institute (PSI), Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland

Montserrat Filella - Department F.-A. Forel, University of Geneva, Boulevard Carl-Vogt 66, CH-1205 Geneva, Switzerland

Contact: roger@hammerdirt.ch

Abstract

[to be completed]

Keywords: Switzerland, Lake Geneva, Bayes theorem, feminine hygiene products, marine-litter, riverine-input, LCA, marine litter indicator

INTRODUCTION¶

According to a Brief History of Marine Litter, the first scientifically recorded interaction between marine organisms and persistent litter was in 1969 {cite}briefhistory. In 1972 the International Journal of Environmental Studies observed that most of the trash on isolated stretches of ocean shoreline was a result of sea‐borne waste; The waste is primarily a by‐product of international commerce and not the behavior of the casual visitor {cite}scottdebunksource. This document picks up the trail 50 years later and several hundred miles upstream. While the harmful effects of plastic are (apparently) debatable, its occurrence on the beach and in the water is undeniable. Volunteers, applying common sense protocols that have been put in place over the past twenty years, have created a very accurate picture of the occurrence of plastics on the beach and on inland lakes and rivers.

The United Nations published a first international guide to collecting ocean beach litter in 2008 {cite}unepseas. This publication was followed by another guide developed by OSPAR {cite}osparguidelines in 2010 and then, in 2013, the EU published the Guidance on Monitoring Marine Litter in European Seas {cite}mlwguidance. Riverine Litter Monitoring - Options and Recommendations was published later, in 2016, as evidence was mounting that rivers are major sources of marine litter. {cite}riverinemonitor As a result, thousands of observations have been collected following a very similar protocol {cite}mlwdata {cite}ospardata. These data are collected by different organizations, mostly volunteer, throughout the European continent. Each observation is a categorical list of objects and their respective quantities within a defined length of shoreline, the EU standard is 100 meters. However, when the baseline values were defined, all samples within a beach length greater than 10 meters were considered {cite}mlwguidance {cite}osparguidelines. The same protocol has been in place in Switzerland since November 2015, targeting regional lakes and rivers. {cite}iqaasl

The data collected by volunteers were considered fit for the purpose of establishing beach-litter threshold values by the Marine Litter Technical Group of the EU. However, the lack of quantitative research on the harmful effects of beach litter, specifically the dose-effect relationship between plastic and ecological harm, precludes the establishment of threshold values based on a health related metric. Quantifying the socio-economic effects prove to be just as diificult. Therefore, threshold values and baselines were adopted according to the precautionary principle {cite}threshholdeu. In practice, EU threshold values are determined by using the 15th percentile (20 p/100m) from the combined data set of the 2015-2016 beach litter surveys within the EU. {cite}threshholdeu

The presence of objects on the shoreline has also raised concern in the Life Cycle Assessment (LCA) community. The Life Cycle Initiative (LCI) is a public-private partnership that includes France, Switzerland, Germany and the EU with a stated goal of advancing the understanding of life cycle thinking by private and public decision makers. In partnership with Plastics Europe, LCI has been attempting to integrate potential environmental impacts of marine litter, especially plastic, in Life Cycle Assessment (LCA) results. {cite}marilca {cite}lci. The consequences of plastic leaked into the environment are not accounted for in the current practice of LCA {cite}woods2021107918. This could be for the same reasons that the EU adopted the precautionary principle, as opposed to the dose-effect relationship when developing threshold values.

Considering that the median value was 133 p/100 m in the 2015-2016 beach litter surveys, it means that regional administrations will need to allocate resources to meet the threshold value if they want to achieve good environmental status under the Marine Strategy Framework Directive {cite}goodenvironmentalstanding. At the same time, producers are considering the risk of the outcome marine-litter and trying to develop strategies to minimize that risk for their own products {cite}plasticorglass {cite}civancikuslu2019621. Determining which are the most effective and efficient solutions will require that both stakeholders conduct intermediate assessments based on benchmarks to evaluate progress and compare probable outcomes. This requires having adequate statistical tools to make reasonable assumptions based on the data.

EU thresholds and LCAs, are attempts at reducing the probability of an object being found but none answers the general question “How likely is an object to be found?”. End Period Plastics in the UK asked this question in preparation for a meeting with producers of FHP in Geneva, Switzerland. The team from End Period Plastics was interested in knowing the incidence of these objects in Lake Geneva {cite}endperiodplastics and allotted three hours of time to do a beach-litter-survey. Tampon applicators and tampons are part of a group of specific items that are found on beaches and most likely originate from toilet flushing or a wastewater treatment facilities, cotton-swabs are also part of that group. {cite}obriain2020116021 {cite}padbackingstrips {cite}increasingplastics

With the inttention of having a successfull event, hammerdirt staff needed to identify the location that had the highest likelihood of finding an FHP within the three hours allotted including the travel time to and from the train station. Beach litter monitoring on Lake Geneva started in November 2015 using the MSFD method {cite}mlwguidance {cite}iqaasl. Data has been collected at irregular intervals all over the lake using the same protocol by different groups since then. Monitoring is also conducted at the Rhône outflow to the Mediteranean at Port Saint Louis. The problem statement is then: Identify the location that has the highest probability of finding at least one FHP.

The resolution to this problem, given the data, is recognising that a quantity is not being requested. What is being requested is a measurement of the risk of encountering a specific object at the beach. What follows is a simple but effective and accurate method to measure that risk and put it in context with the data generating process. The original question, relevant at all times and locations, can be solved within a measure of certainty in the specific case and the general case using common analytical and programmatic tools. How this method was used to answer the question from End Period Plastics and how that method can be used at the regional level is the subject of this paper, starting with the data and methods.

DATA AND METHODS¶

Study sites¶

Lake Geneva is a perialpine lake at an altitude of 372 m above mean sea level located between France and Switzerland. It has an elongated shape, a surface area of 580 km2, and maximum length and width of 72.3 and 14 km, respectively. The average water residence time is 11.3 years. The lake is subdivided into two sub-basins: the Grand Lac (large lake) (309 m deep) and the Petit Lac (small lake) (medium-sized basin with a volume of 3 km3 and a maximum depth of about 70 m. Lake Geneva is fed by a large number of rivers and streams but most of the water enters through the Rhône River. The permanent population (2011) in its watershed is: 1,083,431 (France: 142,229, Switzerland: 941,202) but also hosts a large tourism population. There are 171 wastewater treatment plants (population equivalent: 3,009,830). {cite}cipel2019

Geneva beaches (baby-plage, baby-plage-II, Jardin-botanique, rocky-plage, villa-arton), are located in the Petit Lac (Figure 1). St Sulpice beaches (parc-des-pierrettes, plage- de-dorigny, plage-de-st-sulpice, saint-sulpice, tiger-duck beach), whose data is also used in this study, in the Grand Lac, Map 1.

Lake Geneva is connected to the Mediterranean Sea by the Rhône River. The city of Port Saint Louis is at the mouth of the Rhône where it discharges into the sea. Port Saint Louis benefits from regular monitoring using the same protocol and coding system as Switzerland {cite}merter.

Map one: survey locations in the Petite and Grand lac, November 2015 - Novemeber 2021¶

Data¶

Between November 2015 and November 2021 there were 250 beach-litter surveys at 38 different locations. In total, 78,104 objects were removed and identified, of which 358 objects were either tampons or tampon applicators (0.45) {cite}iqaasl. FHP were present in 103 samples (41%). There were ten locations with only one sample (all sampling periods included), of those ten at least one FHP was identified in four of the ten samples. There are three separate sampling periods, each sampling period represents an initiative or campaign. The sampling periods are not of the same length nor is the sampling frequency fixed, except for a few specific locations in periods two and three.

Project one: 2015-11-15 to 2017-03-01; the first project on Lac Léman (MCBP)
Project two: 2017-04-01 to 2018-05-01; the Swiss Litter Report (SLR)
Project three: 2020-03-01 to 2021-11-01; the start of IQAASL up to two weeks before the survey with End Period Plastics

In Geneva the three locations on the left bank: baby-plage, baby-plage-ii-geneve and rocky-plage are within less than 400 meteres of each other and the accessble shoreline is unimpeded from one location to the next. The three sampling locations were defined by sampling the shoreline starting from baby-plage-geneva and proceeding upstream and marking each 100 meters as a new survey location. Thus, the results for the three locations are considered as one survey location for this analysis and given the name left-bank. The locations on the right bank: jardin-botanique and villa-barton are separated by a greater distance and their is no way to sample the shoreline continuously from one location to the next. These locations are considered independently and as a group. The cumulative number of samples and the number of times an FHP indentified was indeitified is Table 1.

$$ Table 1: \text{The number of samples and the number of times at least one FHP was identified} $$

location	period 1 (t,n)	period 2 (t,n)	period 3 (t,n)	total (t,n)
left-bank	(0,0)	(0,0)	(3,14)	(3, 14)
right-bank	(3,13)	(0,0)	(1,2)	(4,15)
jardin-botanique	(2,3)	(0,0)	(0,0)	(2,3)
villa-barton	(1,10)	(0,0)	(1,2)	(2,12)

Assumptions

The samples are independent and identically distributed
Theta is approximately equal for all locations which is the expected value for the lake
The expected result for the lake or the region is the best estimate for locations without samples
Exchangeability of data {cite}bayesgelman

Computational methods

The Beta - Binomial model is used to determine the probable ratio of the number of times an object is found or not found. The Beta distribution is conjugate to the Binomial distribution which results in a proper posterior distribution that can be solved analytically {cite}bayeskruschke {cite}bayesdowney {cite}bayespilon . The implementation is done with SciPy v1.7 {cite}scipy and pandas v1.34 {cite}reback2020pandas all running in a Python v3.7 {cite}python environment.

The data and methods are available in the repository: https://github.com/hammerdirt-analyst/finding-one-object

Statistical methods¶

Beta - Binomial conjugate model¶

The beach litter is a series of independent experiments that indicates whether an object t was found at a survey. The results of n=250 experiments can be described by the probability mass function (PMF) of the Binomial ditribution. Let T be a random binomial variable of n trials and t successes, success defined as finding at least one FHP:

$$ \begin{equation*} T = f(t,n,p) = Pr(t; n, p) = Pr(X=t) = {n\choose t}p^t(1-p)^{n-k}, 0\leq t\leq n, n\geq 0 \tag{1} \end{equation*} $$

The PMF depends on p which comes from the data. However the true value of p, the probability of finding an FHP, is most likely different than the survey results. To get an answer for p consider that: (i) p is a random variable, (ii) p is defined between 0 and 1 (iii) p is a ratio of the sample space. {cite}thinkbayes2 {cite}jaynes. Let $p=\theta =$ the probability of finding an FHP on the beach and D = the set of survey results (2).

$$ \begin{align} P(\theta|D) &= \frac{P(D|\theta)P(\theta)}{P(D)}, D=\left[\left(t_{i} \cdots, t_{n} \right) \right], t= \begin{cases} t=0\\ t=1 \end{cases} \tag{2} \\[12pt] \text{posterior distribution} &= \frac{\text{likelihood * prior}}{\text{total probability}} \tag{3} \\[12pt] \end{align} $$

Conditioning $\theta$ on D using Bayes rule (2) should give a result very close to t/n (1). Probability notation is easy to resolve visually and the notion of prior knowledge is captured in the expression $P(\theta)$ (2) which is the key to Bayes rule (3). The numerator in (2), $P(D|\theta)P(\theta)$ is the product of two probability distributions, (i) the likelihood $P(D|\theta)$ and (ii) the prior $P(\theta)$. The likelihood is the PMF from equation one (1), the prior is a Beta distribution of any additional knowledge about $\theta$ for FHP on the lake (5). Prior to November 2015 there was no organized data collection of beach litter, the presence of litter had been established on the lake shore but not in the detail needed to develop reasonable assessments. Therefore the assumption is that the probability of finding an FHP on the beach prior to collecting data was =$P(\theta)$ = 0.5 = Beta(1,1) an uninformed conjugate to the Binomial distribution (5). {cite}gelman {cite}jaynes

$$ \begin{align} \text{likelihood * prior} &= P(D|\theta)P(\theta) \tag{4} \\[12pt] &= \left({250\choose 103}\theta^{103}(1-\theta)^{250-103} \right)\left(\frac{1}{Beta(1,1)}\theta^{1-1}(1-\theta)^{1-1} \right) \tag{5} \\[12pt] &= \frac{1}{Beta(1, 1)} {250\choose 103} \theta^{1 + 103-1}(1-\theta)^{1 + 250 -103 -1} \tag{6} \\[12pt] &= \frac{1}{Beta(1, 1)} {250\choose 103} \theta^{1 + 103-1}(1-\theta)^{1 + 250 - 103 -1} \tag{7} \\[12pt] &= \theta^{1 + 103-1}(1-\theta)^{1 + 250 - 103 -1} \tag{8} \\[12pt] \text{total probability} &= P(D) \tag{9} \\[12pt] &= \int_{0}^{1} f(\theta)g(t|\theta) d\theta \tag{10} \\[12pt] &= \frac{1}{Beta(1, 1)} {250\choose 103} \frac{\Gamma(1 + 103) \Gamma( \beta + 250 - 103)}{\Gamma(1 + 1 + 250} \tag{11} \\[12pt] &= \frac{1}{Beta(1, 1)} {250\choose 103} \frac{\Gamma( 1 + 103) \Gamma( 1 + 250 - 103)}{\Gamma(1 + 1 + 250)} \tag{12} \\[12pt] &= \frac{\Gamma( 1 + 103) \Gamma( 1 + 250 - 103)}{\Gamma(1 + 1 + 250)} \tag{13} \\[12pt] \text{posterior distribution} = P(\theta|D) &= \frac{\Gamma(1 + 1 + 250)}{\Gamma( 1 + 103) \Gamma( 1 + 250 - 103)}\theta^{1 + 103-1}(1-\theta)^{1 + 250 - 103 -1} \tag{14} \\[12pt] \end{align} $$$$\text{Beta(103, 147), expected value = 0.409}$$

The numerator simplifies by combining like terms and adding up the exponents (4-7), the result is the original equation. The constants ${250\choose 103}. The expression for the posterior distribution of P($\theta$|D) (11) is the prior distribution including the parameters from the likelihood. While each location may have a different value of $\theta$, it is assumed that the expected value for the lake, $E[ \theta_{lake}]$ is a reasonable starting point for determining the expected value of $\theta$ for locations on the lake.

Results and discussion¶

There are many different ways of approaching the problem. The data from the most recent sampling period on Lake Geneva claims 67 applicators (G96) and 8 tampons (G144) were identified out 27'462 objects. The median number of FHP per 100m was .24 and .05 respectively compared to 400 p/m when all objects are considered. FHP represent a very small portion of the total number of objects found. Consequently, where they are found and how likely they are to be found is of particular importance when trying to reduce the probability of "I found one on the beach today".

To identify the location where the probability of finding one is highest, all locations start with the same assumption $beta(1,1)$. From there each point is updated sequentially with the value of $(\alpha = t, \beta = n - t)$ for each sampling period. If this is considered a local problem then only the results from the municaplities where one was found would be concerned, on a regional scale everybody has a stake and therefore an aggregated value for the region would be a good starting point. Another consideration maybe the density, for example answering the question "Which location has the highest probability above a given quantity ?".

Independent of the other results from the lake and assuming that locations with no samples during a sampling period have no changes. The location with the greatest $E[\theta]$ also has the greatest $var(\theta)$, Table 2 and Figure 3.

$$ \text{Table 2 : The posterior distribution and the expected value with prior} = Beta(1,1) $$

location	period 1 ($\alpha$, $\beta$)	period 2 ($\alpha$, $\beta$)	period 3 ($\alpha$, $\beta$)	E[$\theta$]	var($\theta$)	[.5, .95]
left-bank	Beta(1, 1)	Beta(1, 1)	Beta(4, 12)	0.25	.01	(0.09, 0.43)
right-bank	Beta(4, 11)	Beta(4, 11)	Beta(5, 12)	0.32	.01	(0.16, 0.50)
jardin-botanique	Beta(3, 2)	Beta(3, 2)	Beta(3, 2)	0.55	.04	(0.24, 0.91)
villa-barton	Beta(2, 10)	Beta(2, 10)	Beta(3, 11)	0.21	.01	(0.06, 0.41)

However, assumptions two and three require that the lake data be taken into consideration. Therfore, the prior distribution for each location is the same, $P(\theta_{lake})$ and the results from Table one - period 3 beocome the likelihood, Table 3 & Figure 1. This changes the value of $\alpha$ and $\beta$ for the posterior distribution. The expected values center around .41 and variance decreases by an order of magnitude.

$$ \text{Table 3 : The posterior distribution with prior} = Beta(104, 148) $$

location	period 3 ($\alpha$, $\beta$)	prior	posterior	E[$\theta$]	var($\theta$)	[.5, .95]
left-bank	(3, 11)	Beta(104, 148)	Beta(107, 159)	0.40	.001	(0.35, 0.45)
right-bank	(4, 11)	Beta(104, 148)	Beta(108, 159)	0.41	.001	(0.35, 0.45)
jardin-botanique	(2, 1)	Beta(104, 148)	Beta(106, 149)	0.42	.001	(0.37, 0.47)
villa-barton	(2, 10)	Beta(104, 148)	Beta(106, 158)	0.41	.001	(0.35, 0.45)

Water currents, play a big role in the distribution of objects that have a density $ \leq 1$. The surface currents of Lake Geneva show regions where the water may reside for a sustained period of time because of the interaction of the topography and wind driven currents. By maintaining assumption two and three and accepting more uncertainty the weight of the lake prior can be reduced by optimizing $\alpha and \beta$ for the lake to the lowest possible values that still have an expected value of $E[.41]$, Table 4 & Figure 2.

$$ \text{Table 4 : The posterior distribution with scaled prior} = Beta(9.59, 13.64) $$

location	period 3 ($\alpha$, $\beta$)	prior	posterior	E[$\theta$]	var($\theta$)	[.5, .95]
left-bank	(3, 11)	Beta(9.59, 13.64)	Beta(12.59, 24.64)	0.34	.005	(0.23, 0.47)
right-bank	(4, 11)	Beta(9.59, 13.64)	Beta(13.59, 24.64)	0.36	.005	(0.24, 0.49)
jardin-botanique	(2, 1)	Beta(9.59, 13.64)	Beta(11.59, 14.64)	0.44	.008	(0.3, 0.6)
villa-barton	(2, 10)	Beta(9.59, 13.64)	Beta(11.59, 23.64)	0.33	.005	(0.22, 0.47)

Finding more than two

The litter-survey results are given as the minimum number of objects found, indicating that the probable number of FHP per survey is not limited to one or zero. This corresponds to the assumptions of the litter surveyors and the observation that the more there are on the ground the more often it is likely to be identified. Applying the same methods as table two and four but condtioning D on the number of surveys where $FHP > 2$ gives the following results, Table 5 and Figure 4:

$$ \text{Table 5: Finding more than two FHP at a survey, prior } = Beta(0.12, 0.48) $$

location	period 3 ($\alpha$, $\beta$)	prior	posterior	E[$\theta$]	var($\theta$)	[.5, .95]
left-bank	(1, 13)	Beta(9.59, 13.64)	Beta(10.59, 26.64)	0.28	.005	(0.17, 0.41)
right-bank	(2, 13)	Beta(9.59, 13.64)	Beta(12.59, 26.64)	0.30	.007	(0.19, 0.43)
jardin-botanique	(1, 2)	Beta(9.59, 13.64)	Beta(10.59, 15.64)	0.40	.008	(0.25, 0.56)
villa-barton	(1, 11)	Beta(9.59, 13.64)	Beta(10.59, 24.64)	0.30	.005	(0.18, 0.43)

Saint Sulpice

The shores of Saint Sulpice (Grand Lac) have been monitored yearly since 2016. Contrary to locations in Geneva city, in Saint Sulpice there is only one sample per location per year, apart from tiger-duck beach, which had two samples in year five. Similar to the results from Geneva with a scaled prior, the mean value of theta for the locations in Saint Sulpice is higher than theta lake Figure 5-8, Table 6.

$$ \text{Table 6 : Saint Sulpice posterior distribution with scaled prior} = Beta(9.59, 13.64) $$

location	period 3 ($\alpha$, $\beta$)	prior	posterior	E[$\theta$]	var($\theta$)	[.5, .95]
parc-des-pierrettes	(4, 0)	Beta(9.59, 13.64)	Beta(13.59, 13.64)	0.49	.008	(0.35, 0.65)
plage-de-dorigny	(1, 0)	Beta(9.59, 13.64)	Beta(10.59, 13.64)	0.44	.009	(0.29, 0.60)
plage-de-st-sulpice	(2, 2)	Beta(9.59, 13.64)	Beta(11.59, 15.64)	0.43	.008	(0.29, 0.58)
saint-sulpice	(0, 1)	Beta(9.59, 13.64)	Beta(9.59, 14.64)	0.40	.005	(0.25, 0.56)
tiger-duck-beach	(3, 2)	Beta(9.59, 13.64)	Beta(12.59, 15.64)	0.45	.005	(0.30, 0.6)

The answer: where to sample?

It was decided that the best chances of finding an FHP on Geneva beaches was on the right bank starting with Villa Barton and then proceeding to jardin-botanique if none were found. The locations on the left bank had only 3/14 positive samples in the most recent sampling period, well below the mean for the lake. Furthermore, $E[\theta]$ for FHP > 2 was also higher on the right bank. It takes more time to get to the left bank and there is not a corresponding increase of $E[\theta]$.

Cotton buds or cotton swabs are found in 81% of all surveys on Lake Geneva {cite}iqaasl and mostly originate from the same source as FHP: toilets and wastewater treatment facilities. When cotton swabs are considered the difference between villa-barton and the other locations is more evident. The expected value of theta is highest and the 94% HDI is smallest (support 1a). Supporting the decision to survey the right bank as opposed to the left bank because the occurrence of objects with the same source is also elevated.

When just the results from the sub-basins are considered the range of the 94% HDI increases both in Saint Sulpice and Geneva, reflecting the increase in uncertainty because there is less data being used to assess the probable values of theta. In Geneva the locations that have the fewest surveys (rocky-plage, baby-plage-ii) also had negative survey results for FHP in the most recent sampling period. Consequently, the expected value of theta is lowest at these locations but very close to baby-plage and the expected value for the Petit Lac (figure 3).

The probability of FHP in Saint Sulpice is greatest when just the results from the Grand Lac are considered. In Geneva the expected value is less than the lake when just the results from Petit Lac are considered. This supports the belief that the probability of finding an FHP is lower in Geneva than the lake and most likely lowest on the left bank (figure 3). Making the right bank of the Petit Lac in Geneva the best choice for finding an FHP with a mean value of 35% and most likely between 26% and 43% (Figure 3, Figure 4).

ENVIRONMENTAL POLICY IMPLICATIONS¶

It can be inferred that there is a real chance of finding an FHP anywhere along the Rhône between Geneva and Port Saint Louis, cotton-swabs are even more likely. The rate at which these objects occur is not equal, but it is approximately the same at Port Saint Louis and Saint Sulpice.

The differences between regions can be appreciated using probabilistic methods, adding context to the variance that is observed at a larger scale. Even when the data is restricted to a subset, the analysis leads to the same inferences with varying degrees of certainty. However, uncertainty can be minimized by increasing the number of samples within the region of interest.

Fortunately, the process of collecting samples is an excellent method for stakeholders to build consensus. Beach litter surveys and the protocol have been in service for over 12 years and data collection is often assured by the end user. If a beach-litter survey is considered as customer feedback, then we have presented another method to quantify that feedback with respect to the experience of the end-user.

That these results correspond with the experience of the surveyors follows from the math. The cumulative effect of collecting data is captured in the relationship of the number of times that the event happened to the number of times that it didn't. Bayes theorem facilitates the incorporation of prior knowledge and the MCMC routines describes the probability space directly.

In this example the event was any number greater than zero, however any reasonable integer value could be used. Measuring both the likelihood of the event and the magnitude.

The rates of occurrence are similar between Port Saint Louis and Saint Sulpice however, the rates of consumption are difficult to compare. With inland lakes there are many inputs, but they are limited by the river basin itself, for Port Saint Louis we would need to consider the whole Mediterranean Sea. In general terms the monthly input of FHP to Lake Geneva could be summarized by the usage patterns of females 12-52 years old that live in the Rhône River basin upstream of the Mont Blanc bridge (approximately 500, 000).

In this example a very precise communications package and reduction measures could be elaborated for a very diverse group of end-users within a defined geographic range. The effects of that campaign can be measured directly within the geographic bounds it was intended. Expectations or benchmarks can be based on reasonable results given the data.

Application to the LCA is obvious. The number of FHP used is a function of the number purchased. Thus, the FHP found on the beach in Geneva represents a % of all the FHPs that were used upstream of the bridge. As a result, the probability of an object being found on a beach can be put in relation to how many were sold within a geographic range. Providing a reliable metric to measure return on investment in projects designed to improve end of life-cycle outcomes.

These are direct benefits of collecting data in the field and reporting the results as a likelihood or expectation. These often-overlooked advantages impart four critical pieces of information to the decision maker:

What the status was = ratio of number found to number of samples
What it would most likely be today = the probability distribution of point one
The source of the information = the name of the person who observed the data
How certain the results are = the 94% HDI

If the survey results are considered reliable, stakeholders have a method to anticipate the user-experience and enact policies to improve that experience. This places the assessment of quality and satisfaction into the hands of the end-user.

For producers of goods that appear on beach-litter surveys there is now a method to determine how likely a product will end up on a survey. This gives another metric to determine the accuracy of the Lifecycle Assessment and improve product outcomes with respect to end-of-life.